a. If sin 𝜃 =−1/2, 0° ≤ 𝜃 ≤ 360°, in which quadrants could the terminal arm be located?

b. Draw a labeled diagram to show each case.

1 answer

a. The values of sin 𝜃 =−1/2 correspond to the angles 𝜃 = 210° and 𝜃 = 330° in quadrants III and IV respectively.

b. Here is a labeled diagram showing each case:

In quadrant III (𝜃 = 210°):
- The terminal arm is in the third quadrant.
- The angle between the terminal arm and the x-axis is 210°.
- sin 210° = -1/2.

In quadrant IV (𝜃 = 330°):
- The terminal arm is in the fourth quadrant.
- The angle between the terminal arm and the x-axis is 330°.
- sin 330° = -1/2.

In both cases, the terminal arm intersects the unit circle at a point where the y-coordinate is -1/2.